Journal of Marine Systems 139 (2014) 261–275

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Journal of Marine Systems

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Modelling dinoflagellates as an approach to the seasonal forecasting of bioluminescence in the North Atlantic

Charlotte L.J. Marcinko a,b,⁎, Adrian P. Martin b,JohnT.Allenc a Ocean and Earth Sciences, University of Southampton, University of Southampton Waterfront Campus, Southampton SO14 3ZH, UK b National Oceanography Centre, European Way, Southampton SO14 3ZH, UK c School of Earth and Environmental Sciences, University of Portsmouth, Burnaby Building, Burnaby Road, Portsmouth, Hampshire PO1 3QL, UK article info abstract

Article history: Bioluminescence within ocean surface waters is of significant interest because it can enhance the study of subsur- Received 30 January 2014 face movement and organisms. Little is known about how bioluminescence potential (BPOT) varies spatially and Received in revised form 19 May 2014 temporally in the open ocean. However, light emitted from dinoflagellates often dominates the stimulated biolu- Accepted 30 June 2014 minescence field. As a first step towards forecasting surface ocean bioluminescence in the open ocean, a simple Available online 6 July 2014 ecological model is developed which simulates seasonal changes in dinoflagellate abundance. How forecasting seasonal changes in BPOT may be achieved through combining such a model with relationships derived from Keywords: Bioluminescence observations is discussed and an example is given. The study illustrates a potential new approach to forecasting Dinoflagellate BPOT through explicitly modelling the population dynamics of a prolific bioluminescent phylum. The model Ecosystem developed here offers a promising platform for the future operational forecasting of the broad temporal changes Model in bioluminescence within the North Atlantic. Such forecasting of seasonal patterns could provide valuable infor- Forecast mation for the targeting of scientific field campaigns. Atlantic © 2014 Natural Environment Research Council (NERC). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/).

1. Introduction 2000 km) or forecasting changes in its spatial distribution on time scales of the order of days (Ondercin et al., 1995; Shulman et al., 2003, 2011, Many marine organisms are capable of producing visible light, known 2012). Models have been based upon empirical relationships between as bioluminescence (Haddock et al., 2010; Widder, 2010). Biolumines- bioluminescence and other biogeochemical environmental variables cence is ubiquitous throughout the world's oceans and in certain condi- such as chlorophyll (Ondercin et al, 1995) or the advancement of the tions, highly visible displays of blue light (474–476 nm) can be bioluminescence field through physical advective and diffusive process- stimulated via hydrodynamic stresses induced by surface and sub- es (Shulman et al, 2003, 2011). These models have had limited success surface movement (e.g. Fig. 1). In situ measurement of bioluminescence in simulating the distribution of the bioluminescence field (reviewed offers a number of applications for assessing the wider ocean environ- in Marcinko et al., 2013a). The lack of success indicates that the distribu- ment (Herring and Widder, 2001; Moline et al., 2007). This includes the tion of bioluminescent organisms will not always coincide with that of study of subsurface physical dynamics such as internal waves (Kushnir the phytoplankton dominating the chlorophyll signal or be correlated et al., 1997) and the evaluation of fish stocks using intensified cameras with physical properties. The ecological and behavioural dynamics of at night to identify fish schools (Churnside et al., 2012; Squire and the bioluminescent organisms themselves must be considered for the Krumboltz, 1981). Thus, the ability to forecast its occurrence in surface forecasting of bioluminescence to be improved (Shulman et al., 2012). waters and to assess when the illumination of near-surface motion may Bathyphotometer measurements of flow stimulated biolumines- occur is of significant interest. cence provide a measure of the bioluminescent potential (BPOT) of a Previous attempts to model bioluminescence have focused upon volume of water. Field measurements indicate that dinoflagellates are simulating its distribution over relatively large spatial scales (1000– a major source of bioluminescence and that their light emissions often dominate the BPOT measured in the surface ocean (Batchelder and Swift, 1989; Lapota et al., 1992; Latz and Rohr, 2005; Neilson et al., 1995; Seliger et al., 1962). Although only a small proportion of dinofla- gellates are known to be bioluminescent (around 70 out of approxi- ⁎ Corresponding author. Tel.: +44 2380 596338. E-mail addresses: [email protected] (C.L.J. Marcinko), [email protected] mately 1500 species) a number of studies have found positive (A.P. Martin), [email protected] (J.T. Allen). associations between BPOT and total dinoflagellate cell abundance (i.e. http://dx.doi.org/10.1016/j.jmarsys.2014.06.014 0924-7963/© 2014 Natural Environment Research Council (NERC). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 3.0/). 262 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275

majority of BPOT stimulated in the surface oceans. As part of the LAMP project, this study describes the development, parameterisation and testing of an ecosystem model which simulates broad temporal changes in dinoflagellate abundance within an open ocean region of the North- east Atlantic. The study aims to illustrate how such a model could pro- vide a platform for the future operational forecasting of surface BPOT within the North Atlantic. We take a purposefully simplistic modelling approach combined with the limited available bioluminescence data to conceptualise how the forecasting of surface BPOT could be advanced in the future.

2. Study area

Fig. 1. Dolphins illuminated by dinoflagellate bioluminescence at night as they swim The model aims to simulate a typical annual cycle (for the years be- through the ocean (provided by Ammonite Films). tween 2001 and 2007) within the waters surrounding the Porcupine Abyssal Plain sustained observatory; the black box shown in Fig. 2 based on the standard area E5 of the Continuous Plankton Recorder Sur- bioluminescent plus non-bioluminescent species). For instance, within vey (CPR). This region is characterised by a large spring phytoplankton the Mediterranean and Black Seas a compilation of over 3500 bloom (Ducklow and Harris, 1993) dominated by diatoms (Barlow et al., bioluminescent measurements and 1000 phytoplankton samples 1993; Lochte et al., 1993). The spring bloom is followed by the prolifer- between 1970 and 1995 showed extremely strong positive relation- ation of other organisms (Barlow et al., 1993; Lochte et al., 1993) and ships (r2 = 0.95 to 0.98; p b .05) between BPOT and dinoflagellate cell observations show that dinoflagellates contribute significantly to the abundance (Tokarev et al., 1999). Similarly, positive correlations (r = post bloom summer phytoplankton population (Dodge, 1993; Leterme 0.86–0.93; p b .05) have been found in the mouth of the Vestfjord, et al., 2005; Smythe-Wright et al., 2010). The study region was chosen Norway (Lapota et al., 1989) and the MLML programme, which con- to coincide with previous LAMP experiments (Marcinko et al., 2013b) ducted several cruises in the Irminger Sea between 1989 and 1991 and because of the availability of data required for model optimisation (Marra, 1995), found dinoflagellates were responsible for N90% of and assessment. BPOT throughout spring, summer and autumn (Swift et al., 1995). The findings of the studies described above suggest that temporal changes in dinoflagellate abundance can be used as a proxy for seasonal 3. Model description variations in BPOT. Therefore, explicitly modelling dinoflagellate popu- lation dynamics could provide a feasible approach to operational fore- A schematic of the model including the flows between state vari- casting of BPOT, where ‘operational forecasting’ is the term widely ables is shown in Fig. 3. The model contains five components used to describe the prediction of a specific event using a practical representing the interactions between nutrients, phytoplankton and means. This approach is particularly promising in non-coastal regions zooplankton. The biological ecosystem is assumed to be homogenously where bioluminescent populations are often mixed and modelling distributed within an upper mixed layer overlying a deep abiotic layer. individual species is not possible. A successful dynamical model incor- Organisms are not modelled in the deeper layer as the study is focused porating a ‘dinoflagellate’ functional group will potentially have the ca- upon interactions within the surface waters. The system is composed of pability to reproduce much of the seasonal and large scale spatial two phytoplankton types, diatoms (P1)anddinoflagellates (P2), two nu- variation of the bioluminescence field (Marcinko et al., 2013a). trients, nitrate (N) and silicate (Si), and one predator type, metazoan The modelling of dinoflagellates has largely focused on Harmful zooplankton (Z). Algal Bloom (HAB) species in specific coastal areas (Anderson, 1998; The model provides a simple structure that captures the primary in- Franks, 1997; Montagnes et al., 2008; Olascoaga et al., 2008; Walsh teractions of the ecosystem. Diatoms are included in the model, along et al., 2001) or on dinoflagellates as a functional type in regional coastal with dinoflagellates, because they are known to dominate the spring waters (Cugier et al., 2005; Vanhoutte-Brunier et al., 2008). There have bloom (Barlow et al., 1993; Lochte et al., 1993) and their depletion of been relatively few attempts to model dinoflagellates within the open surface water nutrients can have a strong effect on phytoplankton suc- ocean as they are infrequently regarded as a key species of interest in cession. Other phytoplankton groups are not explicitly included within the basin and global scale models that this environment spans. Whilst the model primarily due to the lack of data available to constrain asso- over the past decade understanding the factors controlling populations ciated model parameters. Differences in the dynamics between phyto- of other phytoplankton groups, such as diatoms, has advanced substan- plankton groups in the model are primarily set through differences in tially, modelling of dinoflagellates, particularly as a mixed population parameter values, which are based on experimental results from species away from coastal areas, is still for the most part in its infancy (Hood within the respective phytoplankton groups. In addition to these differ- et al., 2006). Only in the past decade have larger scale models begun ences in parameters defining key processes such as growth and mortal- to break phytoplankton down into its constituent functional groups ity, dinoflagellates differ from diatoms in the model in terms of sinking. (e.g. Follows et al., 2007; Le Quere et al., 2005; Merico et al., 2004; Modelled diatoms sink from the mixed layer and dinoflagellates do not. Vichi et al., 2007). However, dinoflagellates still tend to be overlooked This difference accounts for many dinoflagellates being motile and within models as they are often considered less important when within the model their ability to maintain their position within the compared to other phytoplankton groups in terms of their role in car- sun-lit mixed layer provides them with an advantage that promotes bon sequestration, remineralisation, nitrification and calcification. Dino- growth. flagellates also, unlike phytoplankton groups such as diatoms, do not Nitrogen is used as the model currency. A fixed N:Si ratio of 1.0666 have a well-characterised defining biogeochemical characteristic, such (Brzezinski, 1985) is assumed. Similarly a C:N ratio of 6.6250, based as silicate limitation, that can be directly modelled and used to define on the widely used “Redfield” ratio (Redfield, 1934), and a constant them as a functional type. Chl:C ratio of 0.0141, a value corresponding to the midpoint of the The Luminescence And Marine Plankton (LAMP) project aimed to range suggested by Behrenfeld et al. (2005) for the north-east Atlantic determine the predictability of bioluminescence through investigating are assumed. Model equations are set out in Appendix A and a full list dinoflagellates—the planktonic functional group responsible for the of model parameters is given in Table 1. C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 263

Fig. 2. Study site surrounding the Porcupine Abyssal Plain; based on standard area E5 of the Continuous Plankton Recorder (CPR) survey.

Physical dynamics controlling the mixed layer depth were not ex- primarily because it is simple enough to be well constrained by the plicitly modelled and no horizontal affects, such as advection, were con- available data yet complex enough to simulate the variable of interest sidered. Observational data have been used to define changes in mixed (dinoflagellate biomass) required for predicting temporal variation in layer depth (MLD), photosynthetically active radiation (PAR) and nutri- BPOT. Knowledge that a process exists does not mean that it has to be ent concentrations directly below the mixed layer as a function of time included in a model to capture first order features of a system. Such an (days), and to drive seasonal changes in the ecosystem. approach can result in a model that is more complicated than necessary The purpose of this study is to develop a model that can be used a (Ward et al., 2013). In the development of all ecosystem models it is first step towards operationally forecasting (i.e. prediction via practical necessary to make simplifying assumptions and strike a fine balance be- means) BPOT. The zero-dimensional model presented is chosen tween capturing the characteristics of the system that are dynamically

Fig. 3. Model schematic stating major coupling processes between state variables. Solid arrows indicate flows of nitrogen between model components within the mixed layer. Dashed arrows indicate input and output from the mixed layer. 264 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275

Table 1 dinoflagellates and diatoms throughout the North Atlantic which can List of parameters used in model containing dinoflagellates for the waters surrounding the be used to investigate relative temporal changes in abundance on sea- Porcupine Abyssal Plain for a typical year within the period 2001 to 2007. sonal or longer time scales (Richardson et al., 2006). Parameter Symbol Unit CPR data within the study region were obtained from the Sir Alister Phytoplankton Hardy Foundation for Ocean Science (SAHFOS) and used to compare ob- −1 fl Maximum growth rate P1 μ1 day served relative seasonal variations in dino agellate and diatom groups μ −1 Maximum growth rate P2 2 day to model output. Total dinoflagellate and diatom abundances per sam- −3 Nitrate half saturation constant P1 kN1 mmol m −3 ple were log10 (N + 1) transformed and averaged for each month of Nitrate half saturation constant P2 kN2 mmol m −3 each year between 2001 and 2007 (following Head and Pepin, 2010). Silicate half saturation constant P1 kSi mmol m −2 −1 −1 Initial P–ISlopeP1 α1 (W m ) day These monthly data were then used to calculate weighted climatologi- – α −2 −1 −1 Initial P ISlopeP2 2 (W m ) day cal averages which ensured that years with a high sampling frequency −1 Sinking rate P1 Vdiatom mday had a larger influence on the mean than those with a low sampling fre- −1 Phytoplankton maximum natural mortality rate mp day −3 quency. Climatological averages were then normalised to a zero mean Phytoplankton mortality half saturation constant kmp mmol m and unit standard deviation z-score (zj) following the method set out Zooplankton in Lewis et al. (2006), Zooplankton maximum grazing rate g day−1 Zooplankton half saturation constant k mmol m−3 z x −μ Zooplankton gross growth efficiency β ¼ j − z j 1 Zooplankton maximum mortality rate ε day 1 σ μ −3 Zooplankton mortality half saturation constant kmε mmol m μ Other where x j is the average value for month j, is the average of all months Remineralisation efficiency τ over the year and σμ is the standard deviation associated with μ −1 Across thermocline mixing coefficient m mday (Cheadle et al., 2003). Normalising the data in this way allows the rela- 2 −1 Light attenuation coefficient due to self-shading kc m (mmol N) − tive seasonal changes in cell abundance captured by the CPR survey to Water attenuation coefficient k m 1 w be compared to the relative seasonal change in biomass simulated by the model. CPR data only provide information on relative changes in abun- important in terms of the model's purpose (Fasham, 1993) and the abil- dance. In order to assess how well the model simulates the absolute ity to adequately constrain parameters and assess model performance phytoplankton abundance, chlorophyll data were compared to the with the observational data available. total modelled phytoplankton biomass (i.e. diatoms + dinoflagellates). Very little observational data were available to constrain other phys- Chlorophyll data were obtained from the standard SeaWiFS product at 9 km ical or biological processes for the period and location of interest. resolution, then log10 transformed to ensure an approximate normal Adding components such as horizontal advection (which requires hori- distribution, and averaged over the study area to form a monthly clima- fi zontal gradients in all elds) or other phytoplankton types to the model tology for the period 2001–2007. that cannot be constrained would increase uncertainty in model results Model simulated nutrient concentrations were compared to ni- (Anderson, 2005). Although simple, the model presented is well trate and silicate monthly climatology data from the World Ocean constrained and able to reproduce the available observations. Further- Atlas 2009 (WOA09). Data were extracted at 1° resolution from more, increasing model complexity would not necessarily lead to im- within the study region at the depth (10 m) most closely corre- fi proved model skill. Signi cant improvement would need to be sponding to the approximate depth at which the CPR instrument is determined statistically through methods such as the Akaike's Informa- towed (~7 m). As with the chlorophyll data, nutrient data were tion Criterion (AIC) which account for extra degrees of freedom. log10 transformed to ensure an approximate normal distribution and averaged over the study area. 4. Observational data 5. Model parameterisation Mixed layer depths (MLDs) within the study region were estimated from Argo profiling float data (www.coriolis.eu.org) for the period 5.1. Model goodness of fit 2001–2007. Estimates were calculated based on a 0.2 °C temperature difference relative to the 10 m depth (de Boyer Montégut et al., 2004) The model was assessed on its combined ability to recreate the rela- for individual profiles and then averaged into a monthly climatology. tive seasonal variation of dinoflagellates and diatoms and the absolute Similarly, PAR data were obtained from the 9 km resolution SeaWiFS seasonal changes in chlorophyll, nitrate and silicate concentrations. A product (http://oceandata.sci.gsfc.nasa.gov). Pixel data from the study cost function was used to assess model performance. It provides a region between 2001 and 2007 were averaged to form a monthly clima- non-dimensional value which quantifies the misfit between model out- tology. To determine below mixed layer nutrient concentrations, nitrate put and observations and is therefore indicative of the “goodness of fit” and silicate monthly climatology data at 1° resolution were obtained (Allen et al., 2007). The closer the cost function is to zero the better the from the World Ocean Atlas 2009 (WOA09; Garcia et al., 2010). Average model is said to perform. nitrate and silicate values within the study region were calculated over Model outputs for chlorophyll, nitrate and silicate were log10 trans- depth ranges corresponding to the estimated MLD ± 1 standard devia- formed and monthly averaged for comparison to observations. In addi- tion. Finally, the climatological estimates for MLD, PAR and below mixed tion, model dinoflagellate and diatom state variables were normalised layer nutrient concentrations were spline interpolated to obtain to a zero mean (Eq. (1)) to allow comparison to corresponding normal- smoothly varying daily estimates for model forcing. ised CPR abundance data. Observations were required for comparison to model output in The cost function is the sum of the misfits between model output order to calibrate model parameters and to assess model performance. and observations over the 5 different data types. The individual misfit In particular the ability of the model to simulate the dynamics of the di- of each data type j is calculated as fl no agellate population was a priority. Long time series data providing 2 information on the temporal variability of phytoplankton are sparse, es- X − 1 yjn ojn pecially regarding dinoflagellates in non-coastal regions. However, the CF ¼ 12 2 j N n¼1 σ 2 Continuous Plankton Recorder (CPR) survey provides data for jn C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 265 where j represents each of the 5 different data types (nitrate, silicate, which the optimiser could search. All parameters in the model were chlorophyll, diatom, dinoflagellate), yjn is the averaged model out- optimised with the exception of the water attenuation coefficient of put in month n of data type j, ojn is the averaged observation in downwelling irradiance (kw) which was set a priori because it is a month n of data type j, σjn is the estimated uncertainty associated well-defined optical property of seawater. Possible ranges for the re- with ojn and N is the total number of observations within each data maining 18 parameters were determined from the literature. Where type over the year (Allen et al., 2007). The cost function is therefore no literature values could be found a deliberately broad range was set defined as to ensure that potential values were not excluded. Fixed values and upper and lower bounds to be considered by the μGA for each parame- X5 ter are shown in Table 2. ¼ : CF CFj 3 j¼1 5.3. Calibration data

It is good practice to parameterise a model with a different dataset to 5.2. Optimisation method the one used for model assessment otherwise the predictive skill of the model cannot be fully evaluated in an unbiased manner. However, this Parameterisation of biological models is notoriously problematic. procedure is often limited by the availability of adequate data (Janssen Many parameter values are poorly constrained and often difficult or im- and Heuberger, 1995). Observational datasets were considered too possible to determine (Franks, 2009). Parameter optimisation tech- small to be split for cross validation purposes. As such, model niques allow parameter values, including those which it might never parameterisation was instead carried out using several sets of synthetic be possible to measure, to be estimated. There are several optimisation data which were comparable to those that would be obtained through techniques available to modellers (Friedrichs, 2001; Kidston et al., 2011; data splitting. Schartau and Oschlies, 2003) which allow a set of parameter values (a Synthetic data were generated based on the statistical properties of parameter vector) to be found which minimises the misfit (as repre- the observational data. First, it was necessary to ensure that observa- sented by the cost function) between model output and a set of calibra- tions of chlorophyll, nutrients and phytoplankton in each month were tion data. In this way it is possible to use abundance and environmental normally distributed (Gaussian distribution). However, environmental data to infer process rates. Here, model parameter values were estimat- observations, particularly those associated with biological processes ed through the use of a micro-genetic algorithm (μGA) following a such as those used here, commonly have a skewed distribution where similar procedure to Schartau and Oschlies (2003).TheμGA is an auto- mean values are low, variances are large and values cannot be negative mated stochastic optimisation technique that operates on a Darwinian (Limpert et al., 2001). Such skewed data frequently demonstrate a log- principal of “survival of the fittest” and is crudely based on the mechan- normal distribution where log(x) is normally distributed. Therefore, ics of genetics (Carroll, 1996; Goldberg, 1989). observational data were log10 transformed and statistical tests were The cost function defined in Eq. (3) was used to assign a cost to pa- performed to ensure data now conformed to a Gaussian distribution. rameter vectors within the optimisation process. To ensure parameter Kolmogorov–Smirnov tests were applied to transformed chlorophyll estimates gained from the μGA were not unrealistic, upper and lower and nitrate monthly data, whilst Shapiro–Wilk tests were used for limits were set for each parameter. These limits defined the range in phytoplankton data as this test is more appropriate for small

Table 2 Parameter ranges defined from the literature for use within the parameter optimisation process.

Symbol Unit Parameter Range Reference

Min Max

Phytoplankton −1 μ1 day 0.4 5.9 Reviewed in Sarthou et al. (2005), Smayda (1997) −1 μ2 day 0.09 2.7 Chang and Carpenter (1994), Juhl (2005), Jeong and Latz (1994), Tang (1996), Hansen et al. (2000), Hansen and Nielsen (1997), Baek et al. (2007), Baek et al. (2008), Smayda (1997) −3 kN1 mmol m 0.1 5.1 Sarthou et al. (2005) −3 kN2 mmol m 0.01 2 Ignatiades et al. (2007), Qasim et al. (1973), Baek et al. (2008), Kudela et al. (2008), Kudela et al. (2010), Seeyave et al. (2009), Kudela and Cochlan (2000) −3 kSi mmol m 0.2 4 Sarthou et al. (2005) −2 −1 −1 α1 (W m ) day 0.001 0.1 Sarthou et al. (2005), Popova and Srokosz (2009), Marañón and Holligan (1999), Denman and Pena (1999), Fasham (1993). −2 −1 −1 α2 (W m ) day 0.001 0.1 Popova and Srokosz (2009), Marañón and Holligan (1999), Denman and Pena (1999), Fasham (1993). −1 Vdiatom mday 0.1 2.5 Sarthou et al. (2005) −1 mp day 0.01 0.5 Fasham (1993), Losa et al. (2004), Merico et al. (2004), Sarthou et al. (2005) −3 kmp mmol m 01

Zooplankton g day−1 0.4 3 Losa et al. (2004), Fasham (1993), Petzoldt et al. (2009), Odate and Imai (2003), Obayashi and Tanoue (2002) −3 kz mmol m 0.01 3 Losa et al. (2004), Sarmiento et al. (1993), Fasham (1993) β 0.1 1 Evans and Parslow (1985), Fasham (1993) ε day−1 0.01 0.5 Losa et al. (2004), Sarmiento et al. (1993), Fasham (1993), Edvardsen et al. (2002) −3 kmε mmol m 00.55

Other τ 0.001 1 m mday−1 0 0.01 Upper limit taken from Fasham (1993) 2 −1 kc m (mmol N) 0.01 0.2 Fasham (1993)

Symbol Unit Value Reference

Fixed parameters −1 kw m 0.04 Fasham (1993), Schartau and Oschlies (2003) 266 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275

retains the broad seasonal trend present in the observational data. An advantage of using synthetic data generation is that it allows a large number of calibration datasets to be obtained, without decreasing the size of the dataset used for model assessment.

5.4. Parameterisation

To parameterise the model, four synthetic datasets were generated. The model was optimised to each synthetic dataset in turn, using the μGA, to obtain four optimised parameter vectors (Table 3). The model was then run using each of the optimised parameter vectors and compared to each of the synthetic datasets using the cost function (Eq. (2)). Parameter vector one led to the lowest total cost when summed over all four synthetic datasets and was therefore considered to perform best. By cross comparing optimised parameter sets tuned to different syn- thetic data in this way, a set of parameters were identified that best rec- reated the broad scale variability in the system. Thus, parameterisation of the model was achieved with limited over-fitting to small scale vari- ances caused by uncertainty in the observed data (i.e. measurement noise) whilst ensuring that the broad scale seasonal variation is reproduced. This is an important step when developing models for op- erational purposes with limited data available. Table 3 indicates that optimum values of several parameters were highly variable across the four optimised parameter vectors. Despite Fig. 4. Example of averaged synthetic dinoflagellate abundance data (x) in comparison to averaged true observational data (o) and associated uncertainty. the variability in many of the parameters, some consistent trends in parameterisation were evident. For example, diatom maximum growth

rate (μ1) was always greater than dinoflagellate maximum growth rate sample sizes (n b 50). Statistical significance was considered at the 95% (μ2), dinoflagellate initial P–I slope (α2) was never larger than diatom (p b 0.05) confidence level. Statistical tests and Quantile–Quantile (Q– initial P–I slope (α1) and dinoflagellate nitrate half saturation constant −3 Q) plots (not shown) indicated that log10 transformed observations (kN2) was always less than 1 mmol N m . were consistent with Gaussian distributions, well described by calculat- ed averages and associated standard deviations. 6. Model dynamics Synthetic data were generated by randomly selecting a number of data points, equal to the number of real observations, from Gaussian Model output obtained using the optimal parameter set is shown in distributions with the same statistical properties of the log transformed Fig. 5. As the MLD shoals and PAR increases in early spring (April), dia- observational data. The synthetic data were then averaged and normal- toms are able to take early advantage of the improving environmental ised in the same way as their corresponding real observations to pro- conditions and increase in biomass, due to their lower affinity for duce a synthetic dataset. An example of synthetic dinoflagellate light. This population growth of diatoms leads to a draw down in both abundance data is shown in Fig. 4 and indicates that synthetic data nitrate and silicate. Dinoflagellates with their higher affinity for light, increase in abundance as the diatoms peak and begin to decline due to increasing silicate limitation. Their lower affinity for nitrate allows dino- Table 3 flagellates to uptake nitrate more efficiently at lower concentrations. Parameter vectors obtained from model optimisation to the four synthetic data sets. Pa- The dinoflagellate population begins to decline in August as nitrate rameter vector 1 is the optimal set of parameters found through the calibration process. levels are drawn down and growth rates become nutrient limited. How- Parameter Parameter Parameter Parameter Parameter ever, as the MLD deepens in September, nutrient levels increase due to vector 1 vector 2 vector 3 vector 4 mixing. This increase in nutrients causes an autumnal increase in both (best) phytoplankton types. Dinoflagellates gain a greater advantage from Phytoplankton the increase in nutrient concentration as their stock biomass in Septem- μ 1 1.45 2.58 3.19 1.53 ber is much higher than that of diatoms which, because of silicate limi- μ 2 0.46 0.55 0.92 0.59 tation during late summer, have decreased to a very low level. k 0.34 4.70 2.64 0.34 N1 It is interesting to note that modelled dinoflagellate biomass stays kN2 0.07 0.17 0.51 0.39 relatively high throughout the year in comparison to diatoms (Fig. 5). kSi 2.37 2.49 1.89 1.59

α1 0.10 0.10 0.10 0.08 Although diatoms dominate the phytoplankton in April and May, dino- α 2 0.06 0.10 0.087 0.05 flagellates dominate at all other times of the year and the magnitude of Vdiatom 0.82 1.17 0.10 1.89 the summer peak in dinoflagellate biomass is larger than that of the m 0.25 0.44 0.35 0.27 p spring diatom peak. Losses in biomass of both phytoplankton groups kmp 0.68 0.75 1.00 0.90 are dominated by zooplankton grazing rather than by natural mortality, Zooplankton indicating that zooplankton are the primary control upon phytoplank- g 1.43 2.55 1.10 2.79 ton biomass (data not shown). kz 1.72 2.48 1.81 1.72 β 0.89 0.60 0.86 0.57 Seasonal changes in zooplankton track changes in phytoplankton ε 0.49 0.38 0.31 0.36 biomass (Fig. 5). Zooplankton grazing contributes significantly to the kmε 0.17 0.04 0.23 0.01 decline of dinoflagellates during August when the zooplankton grazing Other rate exceeds the dinoflagellate growth rate. A high gross growth effi- τ 0.51 0.63 0.60 0.41 ciency coefficient (β) means much of the phytoplankton biomass m 0.01 0.00 0.00 0.0008 grazed is available for zooplankton growth which leads to increased k 0.03 0.05 0.07 0.09 c grazing pressure. C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 267

Fig. 5. Model simulations of seasonal changes in nitrate, silicate, diatom and dinoflagellate biomass, zooplankton biomass and total phytoplankton biomass are shown (reading left to right) for a typical year (2001–2007) in the waters surrounding the Porcupine Abyssal Plain observatory. The bottom right plot shows mixed layer depth (dashed line) and photosynthetically active radiation (solid line) used to force seasonal changes.

7. Model assessment as very good (CFj = b1), using the criteria suggested by Radach and Moll (2006). Monthly averaged outputs are compared to the climatologically Modelled seasonal variation in dinoflagellates shows two peaks, one averaged observations in Fig. 6. The cost function (Eq. (3)), which quan- in mid-summer and a second in autumn. The summer peak corresponds tifies the overall misfit between model simulations and observations is well to the pattern in the observations, whereas the autumnal peak is equal to 1.87. The contribution of the individual data types to the cost not so obvious in the observations, which shows the slow continuous function (CFj; Eq. (2)) are shown in Table 4. These individual compo- decline of dinoflagellates into winter. The model value for dinoflagel- nents can be used to assess the model's ability to simulate the different lates in August lies just outside of the lower uncertainty boundary of observations. Assessment can be made using performance criteria that the observations and is responsible for the two peak pattern observed. are subjectively scaled by the number of standard deviations that The model correctly predicts the seasonal pattern in diatoms showing model simulations are away from the observations (Allen et al., 2007). a peak in early spring. However, a comparison to observations indicates Here, model assessment is made using the performance criteria sug- that the modelled spring diatom bloom may decline too quickly. gested by Radach and Moll (2006) for a cost function as defined in Modelled chlorophyll has a broad primary peak over the spring and

Eq. (2). These criteria are: CFj b 1 is considered very good, 1–2 is good, summer months spanning both diatom and dinoflagellate blooms. Max- 2–3 is reasonable and N3 is poor. These criteria are refined from those imum chlorophyll concentration occurs in June with a secondary peak originally proposed by OSPAR Commission (1998). in autumn (September). This pattern is not exactly equivalent with Fig. 6 shows that the model is able to accurately replicate the timing the observations as the modelled primary peak lags the observations of the main peak in seasonal variability for dinoflagellates (June/July) by two months. However, there are only small differences in average and diatoms (April/May) in the study region. The simulated nutrient observed chlorophyll concentrations between April and June and large and chlorophyll cycles also generally agree well with observations. All associated uncertainties. The secondary autumnal peak in the modelled model variables for which comparable data were available are classified chlorophyll precedes that in the observations by one month. 268 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275

Fig. 6. Comparison of averaged model output (dashed lines and solid circles) against climatologically averaged observations (black triangles). C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 269

Table 4 Light budgets were calculated by multiplying cell abundances of Breakdown of cost indicating misfit between model simulations and observations. bioluminescent species by their approximate flash intensities. Model NitrateSilicateDiatomsDinoflagellates Chlorophyll Total cost Gonyaulax spp. and Ceratium fusus were taken to have flash intensities − forcing of 1 × 108 photons s 1 whilst Protoperidinium spp. were assumed to fl 9 −1 Climatology 0.48 0.29 0.30 0.42 0.38 1.87 ash at an intensity of 1 × 10 photons s (as in Swift et al., 1995). Summing the calculated bioluminescence potential of each genera or species gives an estimate of the BPOT in each month. Over the 2 Modelled mixed layer nitrate concentrations are higher than aver- 2001–2007 climatology a strong positive linear relationship (r = age observations through May to December. However, concentrations .974; p b .001; n = 12) is found between estimated BPOT and total dino- in all months, with the exception of October, are within the variability flagellate abundance within the PAP study region. An assumption can of the observations. Simulated silicate concentrations in the summer then be made that, to first order, cell abundance is directly proportional months of June and July are well matched to their corresponding obser- to biomass such that Biomass =c[Cell Abundance], where c is a constant vations. Modelled silicate is higher than observations through October factor representing the average carbon content per cell. Based on exper- to March but still falls within the observational variability, with the imental data across 20 different dinoflagellate species an average per −1 exception of the December concentration. cell carbon content of 6364 pg C cell is assumed (Menden-Deuer and Lessard, 2000). Using a C:N ratio of 6.625 this is equivalent to 961 pg N cell−1 = 6.86 × 10−8 mmol N cell−1. Using this factor, CPR 8. Modelling inter-annual changes cell abundance is converted to nitrogen biomass and a linear correlation exists between BPOT and nitrogen biomass, as shown in (Fig. 8a). A lin- Given the relatively accurate simulation of the typical seasonal cycle ear regression indicates that BPOT can be approximated by the equation (2001–2007) in dinoflagellate abundance, model analysis was extended BPOT = −8.246 × 1010 +(1.369×1015 ∗ biomass) with an r2 =0.974 to investigate the ability to simulate inter-annual variations over the (p b .001). This relationship can be used to provide a forecast of the sea- same period. Monthly values of MLD and PAR were calculated within sonal change in BPOT given the modelled dinoflagellate biomass as each year from ARGO float and SeaWiFS data respectively. Due to demonstrated in Fig. 8b. there being only limited direct measurements of nutrients over the The example presented here is purely a demonstration based on a study period, below mixed layer nitrate and silicate concentrations model hindcast specific to the Porcupine Abyssal Plain. However, it illus- were again estimated from the WOA09 by taking the monthly climato- trates the potential for this approach to be applied to forecasting the logical value at depths corresponding to below the mixed layer. MLD, seasonal changes in BPOT in future given predictions of the physical PAR and nutrient data were once again spline interpolated to daily environment. Furthermore, comparable model and statistical relation- values (Fig. 7f). Model runs for inter-annual simulations were initialised ships derived from observations could be applied more widely to from the end of a standard 10 year climatological run and used the best other regions of the North Atlantic. Indeed, the observations of dinofla- performing parameter vector (Table 3). Monthly averaged model out- gellate abundance are readily available across the North Atlantic from put was compared to inter-annual monthly observations using the the CPR survey. cost function as in the previous section. Results show that model simulations are robust and can withstand 10. Discussion small changes in forcing (Fig. 7a–e). A breakdown of the cost function indicating the misfit between monthly averaged model simulations The complex and dynamic interactions between bioluminescent and observations from 2001 to 2007 is shown in Table 5. Initially, the plankton, their environment and other organisms have limited the suc- ability of the model to simulate inter-annual changes in dinoflagellate cess of previous attempts to forecast bioluminescence in the North At- and diatom abundance looks poor with cost values N3(Radach and lantic using static relationships between BPOT and variables such as Moll, 2006). However, on closer investigation the large costs can be at- temperature and chlorophyll (e.g. Ondercin et al., 1995). Modelling tributed to just two months in 2004 and 2007 (circled in Fig. 7aandb). the ecological dynamics of bioluminescent organisms and their reac- Particularly large costs are associated with the inability of the model to tions to changes in environment offers a more robust way to forecast simulate the increase of dinoflagellates and diatoms in September 2004 the spatial and the temporal distribution of bioluminescence (reviewed (and similarly the increase of diatoms in July 2007) because only small by Marcinko et al., 2013a). Positive associations between BPOT and total uncertainties are related to the averaged monthly data. It is worth not- dinoflagellate cell abundance including bioluminescent and non- ing that only a few samples (2 and 5) make up the average for these bioluminescent species, found across several regions (Kim et al., 2006; months. Thus, it is possible that the uncertainty on these observations Lapota et al., 1989; Tokarev et al., 1999), indicate that total dinoflagel- is substantially underestimated. Removing the three data points in late abundance can be used as a proxy for BPOT. Given that species of question and recalculating the cost function indicates that model simu- these organisms are responsible for the majority of bioluminescence lations are still classed as very good (b1) or good (1–2) (Table 5). stimulated in the surface ocean of the North Atlantic (Swift et al., 1995), the simple model described above, which is able to simulate di- noflagellate abundance, potentially provides a platform for the future 9. Example BPOT forecast seasonal forecasting of bioluminescence. The model provides a very good fit to monthly climatology observa- Within this section the potential for using output from the model de- tions and is able to recreate both the typical seasonal peak in dinoflagel- veloped in the previous sections to forecast seasonal changes in BPOT is lates and diatoms. However, one concern is that simulations show a two illustrated. To estimate BPOT from model output a relationship between month lag exists between simulated and observed peak chlorophyll BPOT and dinoflagellate nitrogen biomass must be determined. Given concentrations as a consequence of dinoflagellate biomass in summer the lack of BPOT observations with simultaneous abundance/biomass being greater than that of diatoms in spring. This suggests that the data, we determine such a relationship indirectly based on information model underestimates peak diatom biomass or overestimates peak contained within the CPR data for the PAP study area. The dinoflagellate dinoflagellate biomass. Unfortunately, observational data are not avail- abundance data from the CPR survey can be broken down to genera and able to directly compare to simulated biomass estimates of the individ- species level. This allows species that are known to be bioluminescent to ual phytoplankton groups. Nonetheless model results are supported by be identified and an estimate of how BPOT may vary over a typical year data shown by Taylor et al. (1993) taken around 47°N 20°W during May to be constructed. to August 1989, which indicate that estimates of summer dinoflagellate 270 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275

Fig. 7. Comparison between inter-annual model simulations and observational data for (a) normalised seasonal variation in dinoflagellates (b) normalised seasonal variation in diatoms (c) nitrate (d) silicate (e) chlorophyll and (f) inter-annual forcing of MLD and PAR between January 2001 and December 2007. C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 271

Table 5 Breakdown of cost indicating the misfit between inter-annual model simulations and observations.

Model forcing Nitrate Silicate Diatoms Dinoflagellates Chlorophyll Total cost

Inter-annual 0.52 0.24 9.48 6.57 1.54 18.35 Inter-annual (Sep 2004 & Jul 2007 removed) 0.52 0.24 0.82 0.46 1.54 3.58 biomass (~50 mg C m−3 in mid-July) were slightly higher than those for always lower than that of diatoms, in agreement with knowledge that the diatom bloom in late spring (~45 mg C m−3 in mid-May). Laborato- dinoflagellates have lower maximum growth rates than other phyto- ry studies have also indicated that larger dinoflagellates are more car- plankton types of similar size (Banse, 1982; Litchman et al., 2007). bon dense than larger diatoms (Menden-Deuer and Lessard, 2000). It Also, the initial P–I slope of diatoms (α1) was never lower than that of is also possible that the model structure limits its ability to match the dinoflagellates (α2) in agreement with knowledge that diatoms are exact observational pattern in chlorophyll because it does not consider known to generally be better adapted to low-light characteristics (Le other phytoplankton groups such as fast growing phytoflagellates or Quere et al., 2005; Litchman et al., 2007). coccolithophores, which may contribute to the chlorophyll signal in early spring and summer, respectively. 10.1. Forecasting bioluminescence Several parameters show significant variability across the calibrated parameter vectors (Table 3), suggesting some under-determination of Section 9 illustrates how the modelled seasonal changes in dinofla- the system. Uncertainty in the parameter values arises from both vari- gellate abundance can potentially be used to estimate expected BPOT ability in the observations and potential deficiencies of the optimisation at a particular time of year. This was achieved through combining sim- method and model structure (Schartau and Oschlies, 2003). Some of the ulated dinoflagellate biomass data with a statistically derived relation- variability across parameter vectors could be due to the size of the pa- ship between observed dinoflagellate abundance and BPOT. However, rameter ranges used in the optimisation procedure, which were deliber- it must be noted that the estimation of BPOT made here has a number ately broad to ensure that potential values were not excluded (Table 2). of limitations. CPR data are known to underestimate cell abundance Despite the variability across different parameter vectors, several trends due to the sampling procedure and this particularly affects unarmoured were consistent and agree with known physiological traits of the phyto- dinoflagellates. Therefore, results may be biased towards the armoured plankton types. For example, dinoflagellate maximum growth rate was dinoflagellate population and likely substantially underestimate the concentration of bioluminescent cells. Also, in the process of calculating BPOT it is assumed that all cells within a bioluminescent genera or spe- cies will luminesce to their full potential. However, bioluminescent and non-bioluminescent strains of the same species can exist and the phys- iological state of a cell can influence its bioluminescent intensity (Buskey et al., 1994; Latz and Jeong, 1996). Therefore, the modelled BPOT may be lower than calculated. This may be particularly true to- wards the end of a bloom when cells become nutritionally stressed but are still in high abundance. Despite the crudeness of the calculations made in Section 9,itisen- couraging to note that the bioluminescent intensities predicted in this example study are consistent with measurements made during the Ma- rine Light Mixed Layer programme, which found BPOT to vary between approximately 1 × 1014 and 4 × 1014 photons m−3 between May and September within the North Atlantic Irminger Sea (Swift et al., 1995). However, further observations are required to determine a well defined relationship between dinoflagellate abundance and measured BPOT. At present, model calibration and validation are significantly limited by a lack of spatial and seasonal bioluminescence data. The recent develop- ment of commercially available bathyphotometers that can be attached to towed platforms and fixed moorings offers the potential to increase measurement frequency of bioluminescence in the future and efforts should be made to secure sustained observations with the necessary co- incident biological data, particularly at key points in the seasonal cycle such as spring and autumn. Measured BPOT intensities are highly instrument dependent and vary given different flow rates and stimulation mechanisms. Therefore, forecasting exact BPOT intensities stimulated and experienced by an in- dividual observer may be somewhat impractical. However, predicted seasonal changes in dinoflagellate abundance could be used to estimate the probability of encountering bioluminescence at a particular time of year. Model output can be combined with a probability scale, set relative to the magnitude of dinoflagellate abundance above a typical annual mean. An increase in dinoflagellate biomass above the set threshold would be associated with an increased presence of bioluminescent cells and associated with a higher than average likelihood of encounter- Fig. 8. a) Relationship between CPR derived BPOT estimates and dinoflagellate biomass cli- ing bioluminescence at this time of year. matology from the PAP study area between 2001 and 2007 (axes are log10 scaled). b) Ex- ample forecast of BPOT based on modelled dinoflagellate biomass (dashed horizontal line Given that previous research has indicated that forecasting biolumi- indicates seasonal mean). nescence on time scales of hours to days may be heavily dependent on 272 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 modelling its relationship with localised light conditions (Marcinko 11. Conclusion et al., 2013b; Sullivan and Swift, 1995; Sweeney, 1981). The simple example highlighted in Section 9 could be further progressed through The capability to reproduce much of the seasonal variation in biolu- combining finer temporal resolution model output with a biolumines- minescence within the North Atlantic, even if at course resolutions, cence algorithm such as that used by Ondercin et al. (1995), which esti- would be a significant step forward. Forecasting bioluminescence po- mates BPOT within the mixed layer as a function of both simulated tential through modelling the distribution of a specific bioluminescent dinoflagellate biomass and instantaneous solar irradiance at the sea phylum has not previously been attempted. The ability to forecast surface. where and when bioluminescence is most likely to occur, even if the in- tensity itself cannot be estimated, would provide valuable information, 10.2. Future model development currently not available, that may permit enhanced decision making and enable targeted field campaigns. Results have demonstrated the ability of the model to simulate the This study aimed to develop an ecological based model that could be seasonal changes in the dinoflagellate population within an area of the used as a first step in operational forecasting of BPOT. The model suc- Northeast Atlantic, despite its relative simplicity. However, further cessfully simulates broad temporal changes in dinoflagellates (the development and testing of the model in locations other than the planktonic group responsible for the majority of bioluminescence study region will be required before applying it to the wider North observed in surface ocean) for the waters surrounding the Porcupine Atlantic. At present it is not clear to what extent the structural simplicity Abyssal Plain in the Northeast Atlantic. The study has illustrated that of the model may hamper its predictive skill in other locations. The forecasting BPOT may be possible through combining the output of a model lacks terms representing a detrital pool or microbial loop (bacte- relatively simple ecological model with frequently observed statistical ria), which could restrict accurate simulation of recycled nutrient avail- relationships between BPOT and dinoflagellate cell abundance. Howev- ability (Anderson, 2010). These terms may be particularly important in er, further observations of BPOT with coincident dinoflagellate cell oligotrophic regions (such as the subtropical North Atlantic) where abundance data are essential for accurate model validation and predic- nutrient availability is heavily dependent upon recycling in the surface tion. The ability of such an approach to be applied to a wider geograph- layer. The restriction of the model to the mixed layer may also be an ical region has been discussed and, although further work is needed, the issue in such regions, where there may be a significantly deeper phyto- model developed here offers a promising platform for the future opera- plankton community. tional forecasting of bioluminescence in the North Atlantic. The addition of other phytoplankton types, such as small flagellates may improve simulations of chlorophyll and absolute dinoflagellate bio- Acknowledgments mass as in situ observations have shown that they can make up a signif- icant amount of the pre- and post-bloom chlorophyll within the North We acknowledge the Ministry of Defence for their financial support Atlantic (Sieracki et al., 1993; Verity et al., 1993). Correspondingly, the of this project under the Joint Grant Scheme programme (proposal ref: inclusion of protozooplankton may be required for more accurate repre- 1166) and the Natural Environmental Research Council's commitment sentation of the nutrient transfer between small phytoplankton and to the U.K.'s marine research capability through the Oceans 2025 pro- metazooplankton. Furthermore, the inclusion of protozooplankton gramme and NC funding. We thank the Sir Alister Hardy Foundation may improve simulations of recycled nutrient availability as they are for Ocean Science (SAHFOS), David Johns and Darren Stevens and for thought to have an important role in the cycling of organic matter in providing access to, and advice on, data from the Continuous Plankton oceanic waters (Verity et al., 1993). Recorder (CPR) Survey and funding through the SAHFOS associate There is some evidence to suggest that greater phytoplankton com- researcher bursary scheme. We also thank Martin Dohrn and his col- plexity within ecosystem models can generate enhanced portability leagues at Ammonite Films for providing the image used as Fig. 1. (Friedrichs et al., 2007) but this comes at a price. Increasing model com- plexity requires additional observations to constrain parameters and as- Appendix A sess simulations. Additions to the model structure will need to balance the cost in uncertainty and greater need for data against the benefits Mixed layer depth to potential predictive skill. The lack of abundance data for individual phytoplankton groups is known to hinder the calibration and validation Changes in the depth of the mixed layer (M), imposed from observa- of multiple phytoplankton functional type (PFT) models (Hofmann, tions, are a function of time (t) in days and are calculated as 2010). However, methods to identify PFTs from satellite derived dM datasets are continually advancing and may, in future, provide data for htðÞ¼ : A:1 robust model testing of the horizontal distributions of specific phyto- dt plankton types such as dinoflagellates (Aiken et al., 2007; Alvain et al., A positive change in M caused by a deepening in MLD, defined by 2008; Raitsos et al., 2008). h+(t)(Eq.(A.2)), produces entrainment and mixing of nutrients from Forecasting dinoflagellates on finer horizontal scales, with the front the deep abiotic layer into the upper mixed layer. and eddy populated mesoscale of particular interest or below the mixed layer, will require the model structure to be coupled with a þ h ðÞ¼t maxðÞ hðÞ t ; 0 : A:2 more detailed physical model that accurately represents changes in the physical environment at the required spatial scale. This may be achieved by implementing the model into a 3-D ocean general circula- Phytoplankton tion modelling (GCM) framework such as NEMO (Nucleus for European Models of the Ocean; Madec, 2008). The differential equations for phytoplankton state variables have a The model presented in this study, although simple in terms of struc- common form following ture, provides a first step in developing simulations of the broad tempo- fl ral and spatial changes in dino agellate abundance across the North dP ¼ Grow−Mort−Graz−Mix−Sink A:3 Atlantic. Given the example set out in Section 9 of how such simulations dt could provide a feasible approach to estimating seasonal changes in BPOT, this model can provide a solid platform to work from for the fu- where Grow is the gain in phytoplankton due to population growth, ture operational forecasting of BPOT. Mort parameterises all losses through non-grazing activity including C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275 273 natural mortality, Graz is the loss due to zooplankton grazing, Mix is the Grazed material that is not assimilated by zooplankton for growth is loss due to changes in M and Sink is the loss due to cells sinking out of assumed lost via messy feeding (MFZ) and available for remineralisation the mixed layer. back into the nutrient pool. MFZ is given as Phytoplankton growth is a function of both nutrient and light limita- fl P þ P tions. The nutrient limited growth of dino agellates (P2) is controlled by MF ¼ ðÞ1−β g 1 2 Z: A:11 Z k þ P þ P the availability of nitrate (Eq. (A.4)), whereas for diatoms (P1)itisinflu- z 1 2 enced by both nitrate and silicate (Eq. (A.5)). The mortality term for zooplankton is the effective closure term of N the model and represents the losses due to both natural mortality and Grow ¼ J P A:4 P2 2 þ 2 N kN2 higher predators which are not explicitly modelled. The MortZ term fol- lows the hyperbolic form given in Fasham (1993) N Si εZ2 Grow ¼ J min ; P A:5 Mort ¼ A:12 P1 1 þ þ 1 Z þ N kN1 Si kSi kmz Z where kN1 and kSi are the half saturation constants for nitrate and silicate where ε is the zooplankton maximum mortality rate and kmz is the half for P1, kN2 is the half saturation constant for nitrate for P2 and J1 and J2 saturation constant for the zooplankton mortality rate. are the light-limited growth rates for P1 and P2, respectively, calculated The MixZ term concentrates or dilutes zooplankton with the shoaling following Evans and Parslow (1985). or deepening of the MLD, respectively. MixZ is given as Mort, Graz and Mix terms for a specified phytoplankton type j are ZhðÞ t given by Mix ¼ : A:13 Z M m P 2 Mort ¼ p j A:6 Pj k þ P m j Nitrate where mp is the maximum natural phytoplankton mortality rate and km The differential equation for nitrate takes the form is the half saturation constant for phytoplankton mortality. dN P j ¼ τ Mort þ Mort þ Mort þ MF −Grow −Grow þ Mix : Graz ¼ g Z A:7 dt Z P1 P2 z P1 P2 N Pj k þ P þ P z 1 2 A:14 where g is the zooplankton maximum ingestion rate and kz is the half As no detritus pool is explicitly modelled, a constant fraction τ of the saturation constant for grazing. material lost from phytoplankton and zooplankton through mortality þ and messy feeding is remineralised directly into the nutrient pool. The m þ h ðÞt P Mix ¼ j A:8 remineralisation efficiency τ sets the export rate from the biologically Pj M active upper layer into the abiotic deep layer. All material not remineralised (equal toðÞ 1−τ Mort þ Mort þ Mort þ MF ) ef- where m represents the mixing due to turbulence between the upper Z P1 P2 z fectively disappears from the model domain and should be considered mixed layer and the deeper abiotic layer. exported, either to higher predators or below the mixed layer. Diatoms actively sink from surface waters. As such, within the model The MixN term specifies the increase in nitrate due to a deepening of P1 are assumed to sink from the upper mixed layer as represented by the the MLD and is given as Sink term in Eq. (A.3) controlled by a constant sinking rate Vdiatom.Dino- flagellates are not considered to actively sink and the model assumes þ m þ h ðÞt that P remains within the upper mixed layer when there is a shoaling Mix ¼ ðÞN −N A:15 2 N M 0 or no change in M. Hence the Sink term for P2 is set to zero.

where N0 is the nitrate concentration bow the mixed layer. Zooplankton Silicate The zooplankton (Z) differential equation has the form The differential equation for silicate takes the form dZ ¼ − − : GrowZ MortZ MixZ A 9 hi dt dSi ¼ τ Mort þ Graz −Grow =R : þ Mix A:16 dt P1 P1 P1 N Si Si where GrowZ is the gain in zooplankton due to population growth through grazing upon phytoplankton, Mort is the loss due to zooplank- Z where MixSi represents the gain in silicate due to mixing and RN:Si is the ton mortality, and Mix represents changes in zooplankton concentra- Z N:Si ratio. MixSi follows the same form as the mixing term for nitrate tion due to the varying depth (M) of the mixed layer. given in Eq. (A.15) replacing N and N0 with Si and S0 respectively. The GrowZ term assumes that zooplankton effectively has equal Within the model zooplankton are assumed not to uptake silicate for grazing preference for P and P phytoplankton types and is defined 1 2 growth and therefore all grazed silicate material (GrowZ + MFZ)isavail- by able for remineralisation back into the system. P þ P ¼ β 1 2 : References GrowZ g þ þ Z A 10 kz P1 P2 Aiken, J., Fishwick, J.R., Lavender, S., Barlow, R., Moore, G.F., Sessions, H., Bernard, S., Ras, J., where g is the zooplankton maximum specific grazing rate, β is the Hardman-Mountford, N.J., 2007. Validation of MERIS reflectance and chlorophyll dur- fi ing the BENCAL cruise october 2002: preliminary validation of new demonstration assimilation ef ciency and kz is the half saturation constant for products for phytoplankton functional types and photosynthetic parameters. Int. J. grazing. Remote Sens. 28 (3), 497–516. 274 C.L.J. Marcinko et al. / Journal of Marine Systems 139 (2014) 261–275

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